Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

Abstract

We propose a new mathematical model of the TNC oscillator and study its impact on the dynamical properties of the oscillator subjected to an exponential nonlinearity. We establish the existence of hyperchaotic behavior in the system through theoretical analysis and by exploiting electronic circuit experiments. The obtained numerical results are found to be in good agreement with experimental observations. Moreover, the new technique on adaptive control theory is used on our model and it is rigorously proven that the adaptive synchronization can be achieved for hyperchaotic systems with uncertain parameters.